Theorems · Theorem · general topology
Function.Surjective.connectedSpace
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [ConnectedSpace α] [inst_2 : TopologicalSpace β] {f : α → β},
Function.Surjective f → Continuous f → ConnectedSpace β- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- IsConnectedproof · cited by 116
- Function.Surjective.range_eqproof · cited by 70
- ConnectedSpacestatement and proof · cited by 37
- isConnected_rangeproof · cited by 3
- connectedSpace_iff_univproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Homeomorph.connectedSpace_iffproof · cited by 1